Minimal Change and Maximal Coherence for Epistemic Logic ... - IJCAI
Minimal Change and Maximal Coherence for Epistemic Logic Program Updates Yan Zhang School of Computing & IT University of Western Sydney Penrith South DC, NSW 1797, Australia E-mail: [email protected] Abstract We consider the problem of updating nonmonotonic knowledge bases represented by epistemic logic programs where disjunctive information and notions of knowledge and beliefs can be explicitly expressed. We propose a formulation for epistemic logic program updates based on a principle called minimal change and maximal coherence. The central feature of our approach is that during an update procedure, contradictory information is removed on a basis of minimal change under the semantics of epistemic logic programs and then coherent information is maximally retained in the update result. By using our approach, we can characterize an update result in both semantic and syntactic forms. We show that our approach handles update sequences and satisfies the consistency requirement. We also investigate important semantic properties of our update approach such as reduction, persistence and preservation.
1 Introduction Logic programming has been proved to be one of the most promising logic based formulations for problem solving, knowledge representation and reasoning, and reasoning about actions and plans. Recent research on logic program updates further shows that logic programming also provides a feasible framework for modeling agents' activities in dynamic environments [Alferes and et al, 2000; Eiter and et al, 2002; Sakama and Inoue, 1999; Zhang and Foo, 1998]. While all current approaches for logic program updates focus on the problem of updating extended logic programs or their variations, updating epistemic logic programs, however, has yet to be explored in the research. By combining knowledge and belief operators into logic rules, epistemic logic programming [Gelfond, 1994] is a powerful representation formalism in logic programming paradigm. It can deal with more difficult problems in reasoning with disjunctive information while traditional disjunctive extended logic programs fail to handle. Furthermore, epistemic logic programs seem more feasible for knowledge reasoning than many other autoepistemic logics [Gelfond, 1994] and has been used as a formal basis for modeling knowledge in action theories, e.g.
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[Lobo et al, 2001]. When we use an epistemic logic program to represent an agent's knowledge base, it is a nontrivial question how the agent's knowledge base (an epistemic logic program) can be updated when new information is received. In this paper, we propose an approach for epistemic logic program updates. Contrary to other logic programs, notions of knowledge and beliefs in epistemic logic programs have strong semantic connections to the standard Kripke structures of modal logics. On the other hand, epistemic logic programs are also sensitive with various syntactic forms. Hence, we believe that a pure model-based or syntax-based approach will not be appropriate to handle epistemic logic program updates. Instead, we require our update formulation to meet three major criteria: (1) an update should be performed on a basis of minimal change semantics to remove contradictory information; (2) based on the minimal change semantics, the update result should have a clear syntactic representation and contain maximal consistent information from previous progrants); and (3) the underlying update procedure should be consistent, that is, updating a consistent program by another consistent program (or a sequence of consistent programs) should generate a consistent result. Our main idea to accomplish these criteria is so called minimal change and maximal coherence which presents both semantic and syntactic features in an update procedure. The paper is organized as follows. Section 2 presents a brief overview on epistemic logic programs. Section 3 develops a formulation for epistemic logic program updates, while section 4 extends this formulation to handle update sequences. Section 5 investigates important semantic properties for our update approach. Finally, section 6 concludes the paper with discussions on related work and future research.
2 Epistemic Logic Programs: An Overview In this section, we present a general overview on epistemic logic programs. Gelfond extended the syntax and semantics of disjunctive logic programs to allow the correct representation of incomplete information (knowledge) in the presence of multiple extensions. Consider the following disjunctive program about the policy of offering scholarships in some university [Gelfond, 1994]: V: r1: eligible(x)
1 Introduction Logic programming has been proved to be one of the most promising logic based formulations for problem solving, knowledge representation and reasoning, and reasoning about actions and plans. Recent research on logic program updates further shows that logic programming also provides a feasible framework for modeling agents' activities in dynamic environments [Alferes and et al, 2000; Eiter and et al, 2002; Sakama and Inoue, 1999; Zhang and Foo, 1998]. While all current approaches for logic program updates focus on the problem of updating extended logic programs or their variations, updating epistemic logic programs, however, has yet to be explored in the research. By combining knowledge and belief operators into logic rules, epistemic logic programming [Gelfond, 1994] is a powerful representation formalism in logic programming paradigm. It can deal with more difficult problems in reasoning with disjunctive information while traditional disjunctive extended logic programs fail to handle. Furthermore, epistemic logic programs seem more feasible for knowledge reasoning than many other autoepistemic logics [Gelfond, 1994] and has been used as a formal basis for modeling knowledge in action theories, e.g.
112
[Lobo et al, 2001]. When we use an epistemic logic program to represent an agent's knowledge base, it is a nontrivial question how the agent's knowledge base (an epistemic logic program) can be updated when new information is received. In this paper, we propose an approach for epistemic logic program updates. Contrary to other logic programs, notions of knowledge and beliefs in epistemic logic programs have strong semantic connections to the standard Kripke structures of modal logics. On the other hand, epistemic logic programs are also sensitive with various syntactic forms. Hence, we believe that a pure model-based or syntax-based approach will not be appropriate to handle epistemic logic program updates. Instead, we require our update formulation to meet three major criteria: (1) an update should be performed on a basis of minimal change semantics to remove contradictory information; (2) based on the minimal change semantics, the update result should have a clear syntactic representation and contain maximal consistent information from previous progrants); and (3) the underlying update procedure should be consistent, that is, updating a consistent program by another consistent program (or a sequence of consistent programs) should generate a consistent result. Our main idea to accomplish these criteria is so called minimal change and maximal coherence which presents both semantic and syntactic features in an update procedure. The paper is organized as follows. Section 2 presents a brief overview on epistemic logic programs. Section 3 develops a formulation for epistemic logic program updates, while section 4 extends this formulation to handle update sequences. Section 5 investigates important semantic properties for our update approach. Finally, section 6 concludes the paper with discussions on related work and future research.
2 Epistemic Logic Programs: An Overview In this section, we present a general overview on epistemic logic programs. Gelfond extended the syntax and semantics of disjunctive logic programs to allow the correct representation of incomplete information (knowledge) in the presence of multiple extensions. Consider the following disjunctive program about the policy of offering scholarships in some university [Gelfond, 1994]: V: r1: eligible(x)
